Use of Reinforcement Learning to Gain the Nash Equilibrium

Reinforcement learning (RL) is a type of machine learning where an agent learns optimal behavior through interaction with its environment. It is a machine learning training method that trains software to make certain desired actions. Nash equilibrium (SNE) is a combination of actions of the different players, in which no coalition of players can cooperatively deviate. Each player chooses the best strategy among all options. Nash equilibrium occurs when each player knows the strategy of their opponent and uses that knowledge. Nash equilibrium occurs in non-cooperative games when two players have optimal game strategies such that no matter how they change their strategy. This paper explores the application of reinforcement learning algorithms within the domain of game theory, with a particular focus on their convergence properties toward Nash equilibrium. We analyze q-learning approach in 2-agent environments, highlighting their capacity to learn optimal strategies through iterative interactions. Our theoretical investigation examines the conditions under which these algorithms converge to Nash equilibrium, considering factors such as learning rate schedules. The insights gained contribute to a deeper understanding of how reinforcement learning can serve as a powerful tool for equilibrium computation in complex strategic environments, paving the way for advanced applications in economics, automated negotiations, and autonomous systems.